A Derivation of the “Bohr Hypothesis” of the Bohr Hydrogen Atom Analysis

The extraordinary success of the Bohr hydrogen atom analysis in 1913 truly was the beginning of the era of the modern physics of the structure of the atom. Among the a priori assumptions by Bohr in his analysis was his famous and unique hypothesis that the only allowed orbits of the electron are such that the angular momentum of the atom is an integral multiple of Planck's constant. The latter then allowed the well‐known determinate solution of the hydrogen atom problem to follow. The phenomenal success of the Bohr analysis and Bohr solution of the hydrogen atom problem also raises the question of whether the “hypothesis” ought to exist, not as an unsatisfying a priori assumption or hypothesis required for solution, but as a natural consequence of the laws of physics itself. The latter is indeed shown as the logical result in this paper when the problem and Bohr's simplified model are looked at from the point of view of the use of an operator for angular momentum, which is consistent with both the laws of physics and relativity (i.e., special relativity).